Easy

VAE Loss: Reconstruction plus KL

~10 mincode completion

Implement vae_loss(x, x_hat, mu, var, beta) returning a scalar.

Examples

Perfect recon and standard-normal latent: 0

Input
vae_loss([[1, 0], [0, 1]], [[1, 0], [0, 1]], [0, 0], [1, 1], 2)
Output
0

MSE 0.5, KL 0, beta ignored

Input
vae_loss([1, 2], [1, 1], [0, 0], [1, 1], 1)
Output
0.5

Recon 1, KL 0.5, beta=2 gives 2

Input
vae_loss([1], [0], [1], [1], 2)
Output
2

Hints

Hint 1

is the natural log, which is what this formula wants.

Hint 2

Make sure you are not returning negative elbo with the wrong sign.

Requirements

  • beta: KL weight

  • Return scalar

Constraints

  • Allowed library: NumPy only

  • Time limit: 200 ms, Memory: 64 MB

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Where this shows up

~10 min

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Python
import numpy as np


def vae_loss(x, x_hat, mu, var, beta):
    """
    Mean reconstruction plus beta * KL to N(0, I).

    Args:
        x, x_hat: arrays of the same shape
        mu, var:  encoder Gaussian parameters
        beta:     KL weight

    Returns:
        scalar
    """
    # YOUR CODE HERE
    pass
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